Which of the following numbers is a multiple of 12? ${41,64,72,88,119}$
Answer: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $41 \div 12 = 3\text{ R }5$ $64 \div 12 = 5\text{ R }4$ $72 \div 12 = 6$ $88 \div 12 = 7\text{ R }4$ $119 \div 12 = 9\text{ R }11$ The only answer choice that leaves no remainder after the division is $72$ $ 6$ $12$ $72$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $72$ $72 = 2\times2\times2\times3\times3 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $72$. We can say that $72$ is divisible by $12$.